A king and a flush draw will bet if you check (massively -EV river play). A king, flush draw and lower pocket pairs will at least call when you bet (less -EV river play). Hence if you are going to showdown you should betfold instead of checkcall so you don't miss value from worst Ks and pocket pairs and well, a higher percentage than most would imagine just ace high.
Explained better check out my posts at the bottom.